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        <td class="header">&nbsp; <span style="font-weight: bold;">IEM Multi-Angle&nbsp;Inversion</span><br>
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<br>
<br>
There is a strong correlation between soil
dielectric and radar backscatter. By inverting the Integral Equation
Model (IEM), the real dielectric constant (RDC) can be obtained from
the radar backscatter coefficient. The inversion is accomplished by
using a Look Up Table (LUT). <span style="" lang="EN">A k-d tree is used to store the LUT for searching.<br><br>To address </span>
the possibility of multiple roots in the model inversion, an
iterative approach is adopted. The first pass produces the closest
match RDC value in each pixel. In the second pass, a representative
first-pass RDC value (mean is used) is derived from a square
neighbourhood centred at the pixel (excluding the centre). This
representative value is compared with the pixel's own first-pass RDC
value. If it deviates too much from its neighbours, it is labelled as
an outlier.<br><br>For each outlier,
the RDC value with the least deviation among the N closest
backscattering coefficients from the LUT is used to replace the
first-pass value. If no such RDC value exists or the deviation is still
too high, then the RDC value is optionally filtered by replacing it
with the representative value. If rms is output, it will also be replaced by its representative (mean) value.<br>
<br>
<span style="font-weight: bold;">Multi-Angle Approach<br>
<br>
</span>The
Multi-Angle approach utiliizes one backscatter coefficient (HH or VV)
from each of the two images (AM or PM). So there are 4 possible
combinations:<br>
<ul>
    <li>HH1-HH2</li>
    <li>HH1-VV2</li>
    <li>VV1-VV2</li>
    <li>VV1-HH2</li>
</ul>
where HH1 and VV1 are from the AM image and HH2 and VV2 are from the PM
image.<br>
<br>
User can select one of the 4 combinations.<br>
<br>
<span style="font-weight: bold;">Calibrated IEM LUT</span><br>
<br>
User can browse for a calibrated <a href="IEM-LUT.html">IEM
    LUT</a>. Matlab (.mat) and CSV (.csv) formats are supported.<br>
<br>
<span style="font-weight: bold;">Parameters Used</span><br>
<br>
The source bands used are one backscatter coefficient (HH or
VV)&nbsp; as well as the local incidence angle from each image.<br><br><span
        style="font-weight: bold;">UI Parameters</span><br><br><span style="font-weight: bold;">N</span> : &nbsp;This is
the number of&nbsp;closest matches to request from the kd-tree.<br><br><span style="font-weight: bold;">M</span>: &nbsp;
This is the length (in pixels) of the side of the square neighbour. It must be odd and greater than 1.<br><br><span
        style="font-weight: bold;">RDC deviation threshold</span>:
&nbsp;The RDC deviation is the absolute difference between the RDC
value and the mean RDC of the neighbourhood pixels, as a fraction of
the mean RDC. This is the threshold above which the pixel is labelled
an outlier.<br><br><span style="font-weight: bold;">Filter remaining outliers</span>: Checkbox for optional filter using
the mean of the neighbouring RDC.<br>
<br>
<span style="font-weight: bold;">Outputs<br>
</span><br>
The RDC from the LUT is output as a band.<br>
<br>
<span style="" lang="EN">User can also optionally
output the RMS roughness height (rms)&nbsp;from the LUT as a band.</span><br>
<br>
If sand and clay percentages are present as source bands, they will be
copied from the input product to the output product.<br><br>An optional outlier band outputs the outlier status of the
pixel:<br>
<ul>
    <li>0 means the first-pass RDC value has not been replaced</li>
    <li>1 means the first-pass RDC value has been replaced by another &#8216;better&#8217; possible root</li>
    <li>2 means &nbsp;the first-pass RDC value has been replaced by the representative value derived from its
        neighbours
    </li>
</ul>
The
output of this optional outlier band is controlled by setting a
preference called "snap.soil_moisture.output_outlier" in the
snap.properties file in &nbsp;the folder
"snap-desktop\snap-application\target\snap\etc".<br>
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